Pre-Algebra Examples

Add:

\frac{5 y}{x} + \frac{3 x}{y}

$\frac{5 y}{x} + \frac{3 x}{y}$

Step 1

To write

\frac{5 y}{x}

$\frac{5 y}{x}$ as a fraction with a common denominator, multiply by

\frac{y}{y}

$\frac{y}{y}$ .

\frac{5 y}{x} \cdot \frac{y}{y} + \frac{3 x}{y}

$\frac{5 y}{x} \cdot \frac{y}{y} + \frac{3 x}{y}$

Step 2

To write

\frac{3 x}{y}

$\frac{3 x}{y}$ as a fraction with a common denominator, multiply by

\frac{x}{x}

$\frac{x}{x}$ .

\frac{5 y}{x} \cdot \frac{y}{y} + \frac{3 x}{y} \cdot \frac{x}{x}

$\frac{5 y}{x} \cdot \frac{y}{y} + \frac{3 x}{y} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of

x y

$x y$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5 y}{x}

$\frac{5 y}{x}$ by

\frac{y}{y}

$\frac{y}{y}$ .

\frac{5 y \cdot y}{x y} + \frac{3 x}{y} \cdot \frac{x}{x}

$\frac{5 y \cdot y}{x y} + \frac{3 x}{y} \cdot \frac{x}{x}$

Step 3.2

Multiply

\frac{3 x}{y}

$\frac{3 x}{y}$ by

\frac{x}{x}

$\frac{x}{x}$ .

\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{y x}

$\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{y x}$

Step 3.3

Reorder the factors of

y x

$y x$ .

\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{x y}

$\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{x y}$

\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{x y}

$\frac{5 y \cdot y}{x y} + \frac{3 x \cdot x}{x y}$

Step 4

Combine the numerators over the common denominator.

\frac{5 y \cdot y + 3 x \cdot x}{x y}

$\frac{5 y \cdot y + 3 x \cdot x}{x y}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

y

$y$ by

y

$y$ by adding the exponents.

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Step 5.1.1

Move

y

$y$ .

\frac{5 (y \cdot y) + 3 x \cdot x}{x y}

$\frac{5 (y \cdot y) + 3 x \cdot x}{x y}$

Step 5.1.2

Multiply

y

$y$ by

y

$y$ .

\frac{5 y^{2} + 3 x \cdot x}{x y}

$\frac{5 y^{2} + 3 x \cdot x}{x y}$

\frac{5 y^{2} + 3 x \cdot x}{x y}

$\frac{5 y^{2} + 3 x \cdot x}{x y}$

Step 5.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 5.2.1

Move

x

$x$ .

\frac{5 y^{2} + 3 (x \cdot x)}{x y}

$\frac{5 y^{2} + 3 (x \cdot x)}{x y}$

Step 5.2.2

Multiply

x

$x$ by

x

$x$ .

\frac{5 y^{2} + 3 x^{2}}{x y}

$\frac{5 y^{2} + 3 x^{2}}{x y}$

\frac{5 y^{2} + 3 x^{2}}{x y}

$\frac{5 y^{2} + 3 x^{2}}{x y}$

\frac{5 y^{2} + 3 x^{2}}{x y}

$\frac{5 y^{2} + 3 x^{2}}{x y}$